Proving Identities

Proving Identities

Tuesday, May 13, 2014

7:52 AM

An "identity" is a tautology, an equation or statement that is always true, no matter what. For instance,sin(x) = 1/csc(x) is an identity. To "prove" an identity, you have to use logical steps to show that one side of the equation can be transformed into the other side of the equation. You do not plug values into the identity to "prove" anything. 

Pasted from <http://www.purplemath.com/modules/proving.htm>

I was not a brilliant Math student but I was a good student studying Math :)

Still, I managed to enjoy some and survived all subjects required for me to graduate the course. In the 13 years that passed, I mastered my pluses and minuses with a bit of multiplications & divisions on the side. MDAS is a mighty weapon for everyday living :D (I surely hope my Professors are not reading this. Else they might file a petition to withdraw my grades. Tsk!)

In our Junior year, we took up Trigonometry. That was about the same time I already kept asking myself whether I was in a wrong place or perhaps in a wrong time. I couldn't fathom why my classmates who would not even take notes ace the exams while I who would copy down the last equation could barely move to item number 2 in our quizzes. I've never felt life to be so unfair. Huhu...Then one morning, when the books were out and the  Prof begun scribbling on the board, I got smitten by a kindred spirit staring back at me. Our lesson that day was Pythagorean Identities. Even to this day, it amazes me how I managed to love and look forward to that topic. And I got correct answers in all quizzes, too! Yep! You read it right, no typographical errors here :D  Man, that was such a mystery. Haha...Let me warn you though, that subtopic only lasted for a week. And we met again only in the Finals. I think I got 2 or 3 questions right of the 50 that we were given. Thanks to my ehem..excellence  with the Identities. Even as I write, I couldn't help suppressing a smile. It was such a pleasant memory; like an oasis in the dessert at the time when I could barely finish the course.

Moving forward, to this present time, somehow the lessons move out from the classroom into the realities of life. Growing up was, and still is, never easy.  I had to put up with a lot of identity crises, playing one role to the next, always trying to fit in. Always trying to be the good neighbor, the good friend, the good sister, the good daughter. What I thought would be good, or would be good in the eyes of my imaginary audience, I readily plugged into my system. Like a trial and error method of taking values of the x's and y's of my life equations. In the end, I got tangled with hypothetical solutions. Slow  maybe, yet, guided by divine grace, growth became a beautiful and happy process. I am no longer in front of all sorts of audience, I am with my loved ones. I need not be good, I only have to do my best for the people  who love and accept me just the way I am. When I was called into this life to be holy, it was to be true first and foremost to my self, of who I am and what am I here for. An understanding where reason meets faith. Always, our dear Professor, Dr. Luna would say "Be guided with logic. Use your common sense". We used to laugh about it and joke about a common sense that is not so common. Truly, even in our walk of faith, always we must be guided by logic. After all, isn't God the most logical and sensible? Even in the midst of a great mystery, always the human mind, touched by divine wisdom, gets to comprehend what is beyond understanding. With our spiritual eyes opened the one truth withheld to many who refuse to see gets revealed. Only in unity with our Creator will we ever find who we are. Only then can the image of man and God be one and the same.